eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
1
22
10.22130/scma.2019.93964.499
37371
مقاله پژوهشی
A New Iterative Algorithm for Multivalued Nonexpansive Mappping and Equlibruim Problems with Applications
Thierno Mohadamane Mansour Sow
sowthierno89@gmail.com
1
Gaston Berger University, Saint Louis, Senegal.
In this paper, we introduce two iterative schemes by a modified Krasnoselskii-Mann algorithm for finding a common element of the set of solutions of equilibrium problems and the set of fixed points of multivalued nonexpansive mappings in Hilbert space. We prove that the sequence generated by the proposed method converges strongly to a common element of the set of solutions of equilibruim problems and the set of fixed points of multivalued nonexpansive mappings which is also the minimum-norm element of the above two sets. Finally, some applications of our results to optimization problems with constraint and the split feasibility problem are given. No compactness assumption is made. The methods in the paper are novel and different from those in early and recent literature.
https://scma.maragheh.ac.ir/article_37371_8562efa14f6c3cc3f1a5bef0e2759b6b.pdf
Multivalued mappings
Equilibrium problems
Iterative methods
Applications
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
23
36
10.22130/scma.2019.97961.527
37373
مقاله پژوهشی
Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions
Mensur Yalcin
tuugbaa@hotmail.co
1
Hakan Simsek
hasimsek@hotmail.com
2
Ishak Altun
ishakaltun@yahoo.com
3
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.
In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the quasi metric does not provide the symmetry property. Finally, we show that our main results includes many fixed point theorems presented on both complete metric and complete quasi metric spaces in the literature. We also provide an illustrative example to show importance of our results.
https://scma.maragheh.ac.ir/article_37373_aad63a7ac585d04a6ecd958a0f67b051.pdf
Quasi metric space
left $K$-Cauchy sequence
left $mathcal{K}$-completeness
Fixed point
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
37
53
10.22130/scma.2018.86797.440
37410
مقاله پژوهشی
Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations
Hasan Hosseinzadeh
hasan_hz2003@yahoo.com
1
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
Let $\mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $\mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $\mathcal{X}$, where $g$ is a function from $\mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. Some applications for linear and nonlinear matrix equations are given.
https://scma.maragheh.ac.ir/article_37410_66eea9cbee3a9a5ccfbce5ff9cbcd2b5.pdf
Fixed points
Coupled fixed point
Coupled coincidence fixed Point
Generalized metric
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
55
68
10.22130/scma.2018.88329.461
37411
مقاله پژوهشی
Some Results on the Field of Values of Matrix Polynomials
Zahra Boor Boor Azimi
zahraazimi1@gmail.com
1
Gholamreza Aghamollaei
aghamollaei@uk.ac.ir
2
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of values of basic A-factor block circulant matrices are investigated.
https://scma.maragheh.ac.ir/article_37411_dde7ec5ae03c9208d9ee594fab1f00a2.pdf
Field of values
Perturbation
Matrix polynomial
companion linearization
Basic $A-$factor block circulant matrix
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
69
82
10.22130/scma.2018.85895.433
37712
مقاله پژوهشی
Vector Optimization Problems and Generalized Vector Variational-Like Inequalities
Ildar Sadeqi
esadeqi@sut.ac.ir
1
Somayeh Nadi
s.nadi229@gmail.com
2
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector variational-like inequalities and vector optimization problems are established.
https://scma.maragheh.ac.ir/article_37712_21815133c068c44f4de658d87ac91628.pdf
Nonsmooth functions
Limiting subdifferential
Pseudoinvex functions
Vector variational-like inequalities
Vector optimization problems
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
83
105
10.22130/scma.2018.92986.488
37412
مقاله پژوهشی
Common Fixed Point Results on Complex-Valued $S$-Metric Spaces
Nihal Taş
nihalarabacioglu@hotmail.com
1
Nihal Yilmaz Ozgur
nyozgur@gmail.com
2
Department of Mathematics, Bali kesir University, 10145, Bali kesir, Turkey.
Department of Mathematics, Bal\i kesir University, 10145 Bal\i kesir, Turkey.
Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems using different techniques by means of new generalized contractive conditions and the notion of the closed ball. Our results generalize and improve some known fixed point results. We provide some illustrative examples to show the validity of our definitions and fixedpoint theorems.
https://scma.maragheh.ac.ir/article_37412_e477c6d8dffcdb074632c412bdb687c1.pdf
$S$-metric space
Fixed point theorem
Common fixed point theorem
Complex valued $S$-metric space
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
107
117
10.22130/scma.2019.69719.273
37414
مقاله پژوهشی
On the Monotone Mappings in CAT(0) Spaces
Davood Afkhami Taba
afkhami420@yahoo.com
1
Hossein Dehghan
hossein.dehgan@gmail.com
2
Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, P.O.Box 79158-93144, Bandar Abbas, Iran.
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava Zang, P.O.Box 45137-66731, Zanjan, Iran
In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods by combining the resolvent method with Halpern's iterative method and viscosity approximation method for finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations in CAT(0) metric spaces.
https://scma.maragheh.ac.ir/article_37414_68347178e93bdca436046052192cf88e.pdf
Monotone mapping
Nonexpansive mapping
Variational inequality
Fixed point
CAT(0) metric space
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
119
138
10.22130/scma.2019.95982.515
38391
مقاله پژوهشی
Best Proximity Point Results for Almost Contraction and Application to Nonlinear Differential Equation
Azhar Hussain
hafiziqbal30@yahoo.com
1
Mujahid Abbas
abbas.mujahid@gmail.com
2
Muhammad Adeel
adeel.uosmaths@gmail.com
3
Tanzeela Kanwal
tanzeelakanwal16@gmail.com
4
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
Department of Mathematics, Government College University, Lahore 54000, Pakistan and Department of Mathematics and Applied Mathematics, University of Pretoria Hatfield 002, Pretoria, South Africa.
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan.
Berinde [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum {\bf 9} (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $\Theta$- contraction mappings andto prove some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $\Theta$-contraction mappings are obtained. Moreover, we give an example to support the results presented herein. An application to a nonlinear differential equation is also provided.
https://scma.maragheh.ac.ir/article_38391_5cea07e80507a72f15663157ce9b5ec2.pdf
Almost contraction
$Theta$-contraction
best proximity points
differential equation
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
139
159
10.22130/scma.2018.94775.506
37469
مقاله پژوهشی
Inequalities of Ando's Type for $n$-convex Functions
Rozarija Mikic
rozarija.jaksic@ttf.hr
1
Josip Pečarić
pecaric@element.hr
2
University of Zagreb, Faculty of Textile Technology, 10000 Zagreb, Croatia.
RUDN University, Miklukho-Maklaya str. 6, 117198 Moscow, Russia.
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribari\v c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
https://scma.maragheh.ac.ir/article_37469_f2353c2142d6389e80c0e9841406ce3f.pdf
Solidarities
Ando's inequality
Edmundson-Lah-Ribariv c inequality
$n$-convex functions
Operator means
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
161
171
10.22130/scma.2018.84950.427
37836
مقاله پژوهشی
New Generalization of Darbo's Fixed Point Theorem via $\alpha$-admissible Simulation Functions with Application
Hossein Monfared
monfared.h@gmail.com
1
Mehdi Asadi
masadi.azu@gmail.com
2
Ali Farajzadeh
farajzadehali@gmail.com
3
Department of Mathematics, Bilehsavar Branch, Islamic Azad University, Bilehsavar, Iran.
Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
Department of Mathematics, Razi University, Kermanshah, 67149, Iran.
In this paper, at first, we introduce $\alpha_{\mu}$-admissible, $Z_\mu$-contraction and $N_{\mu}$-contraction via simulation functions. We prove some new fixed point theorems for defined class of contractions via $\alpha$-admissible simulation mappings, as well. Our results can be viewed as extension of the corresponding results in this area. Moreover, some examples and an application to functional integral equations are given to support the obtained results.
https://scma.maragheh.ac.ir/article_37836_ebd5fb7f6d8fb30eaa38020d459af69d.pdf
Measure of non-compactness
Simulation functions
$alpha$-admissible mappings
Fixed point
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
173
183
10.22130/scma.2019.107061.601
39051
مقاله پژوهشی
Bornological Completion of Locally Convex Cones
Davood Ayaseh
d_ayaseh@tabrizu.ac.ir
1
Asghar Ranjbari
ranjbari@tabrizu.ac.ir
2
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.
https://scma.maragheh.ac.ir/article_39051_31fe870e6a837c4f5f9a112e82686fa3.pdf
Locally convex cones
Bornological convergence
Bornological cones
Bornological completion
eng
University of Maragheh
Sahand Communications in Mathematical Analysis
2322-5807
2423-3900
2020-06-01
17
2
185
201
10.22130/scma.2018.97329.523
37409
مقاله پژوهشی
Generalized Continuous Frames for Operators
Chander .Shekhar
shekhar.hilbert@gmail.com
1
Sunayana Bhati
bhatisunayana@gmail.com
2
G.S. Rathore
ghanshyamsrathore@yahoo.co.in
3
Department of Mathematics Indraprastha college for Women, University of Delhi, Delhi 110054, India.
Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India.
Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India.
In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ \mathcal{H} $ with respect to $ \mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized continuous $K$-frames.
https://scma.maragheh.ac.ir/article_37409_fa26e1468b04482563c581f767572d35.pdf
Frames
K-frames
Continuous frames